Lindenmayer Systems and Global Transformations

Accretive Computation of Global Transformations

“…This issue does not arise in our approach which formally enforces the rules to mutually agree in case of overlap [10]. The cost of this strategy is a multiplication of rules causing an over load of work during computation [5]. As a comparison, the Sierpinski rule system of Fig.…”

“…Refer to [9] for details. These constructions are also pedagogically introduced in the context of global transformation in [5].…”

“…We say that z links g and g ′ through F if the zig-zag F (z) links g and g ′ . In the section, we adapt the definitions of global transformations given in [5,10] to fit with the context of graphs.…”

“…2 for an illustration. The resulting graph is formally the apex of a cocone from the diagram defined in the previous step which we used to obtain by colimit [10,5]. Since colimits are only guaranteed in Graph, we consider the following functor T : GraphI → Graph:…”

“…The applicability of global transformations to capture local, synchronous and deterministic dynamical systems has been shown with examples like dynamic meshes operations, acting on abstract cellular complexes [10], and like deterministic Lindenmayer [5] systems and cellular automata [6], acting on formal words. In parallel of these works, a software development has been undertaken to demonstrate the practicability of the global transformation approach.…”